More than 2500 years ago, the pre-Socratic Greek philosopher Heraclitus stated that the “only thing that is constant is change.” This appears to be a fundamental fact about the world. Nonetheless, even though change itself is an invariant and universal feature of our world, rates and direction of change are variable and unpredictable. Trends end abruptly and discontinuously and patterns are fleeting and illusory. One model that describes historical and natural change processes is the ‘slow-fast-slow’ trajectory of the Sigmoid (S) curve. Events unfold slowly and imperceptibly, then thrust forward exponentially into a new state, and finally recede into a new steady-state. The universe seems to be replete with S-curves, however, they only come into focus retrospectively.
The convexity of the S-curve explains the near universal phenomena such as diminishing returns and marginal utility. Concavity explains the growth of living organisms, positive feedback loops, and compounding returns. Stephen J. Gould’s theory of punctuated equilibrium explains the history of speciation with a S-curve, Joseph’s Schumpeter’s creative destruction can be modeled via a S-curve, Thomas Kuhn’s paradigm shifts can also be explained by S-curves.
In French, the verb essayer means ‘to attempt’ or ‘to embark upon.’ I hope to use the essays on this website to explore, compose, connect, and develop ideas from my readings and experiences. To think is to capture reality by means of ideas” and to write is to think on paper. Learning to write, learning to think, learning itself all follow S – Curves. Slow and imperceptible movement, a phase transition into new mental models, and the process repeats again. As the historian Will Durant stated, “the only real revolution is in the enlightenment of the mind and the improvement of character, the only real emancipation is individual.”